Group Importances

In this notebook we show how to compute and interpret Overall Importances shown in InterpretML’s Global Explanations for EBMs. We also show how to compute importances of a group of features or terms.

Throughout the notebook we use term to denote both single features and interactions (pairs).

This notebook can be found in our examples folder on GitHub.

# install interpret if not already installed
try:
    import interpret
except ModuleNotFoundError:
    !pip install --quiet interpret pandas scikit-learn

Train an Explainable Boosting Machine (EBM) for a regression task

Let’s use the Boston dataset as a reference and train an EBM.

import numpy as np
import pandas as pd
from sklearn.datasets import load_diabetes
from interpret.glassbox import ExplainableBoostingRegressor

from interpret import set_visualize_provider
from interpret.provider import InlineProvider
set_visualize_provider(InlineProvider())

X, y = load_diabetes(return_X_y=True, as_frame=True)

ebm = ExplainableBoostingRegressor()
ebm.fit(X, y) 

ExplainableBoostingRegressor()

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Explain the Model

EBMs provide two different kinds of explanations: global explanations about the overall model behavior and local explanations about individual predictions from the model.

Global Explanation

Global Explanations are useful for understanding what a model finds important, as well as identifying potential flaws in its decision making or the training data. Let’s start by computing and displaying a global explanation:

from interpret import show
show(ebm.explain_global(name='EBM'))

The overall importance for each term is calculated as the average absolute contribution (score) a term (feature or pair) makes when predicting across the training dataset. This way of measuring term importance tends to favor terms which, on average, have large impact on predictions for many cases. The overall importance is not a measure of positive/negative – it is a measure of how important each term is in the scores. For regression, these scores are represented in the same units as the y-axis of the feature graphs. For classification, the scores would be in logits.

Going beyond overall term importances, because EBMs are additive models we can measure exactly how each term contributes to a prediction. Let’s take a look at the graph of the term, bp, by selecting it in the drop-down menu.

The way to interpret this is that if a new datapoint came in with bp = 0.1, the model adds about +33.1 to the final prediction. However, for a different datapoint with bp = 0.13, the model would now add approx. +36.7 to the prediction.

To make individual predictions, the model uses each term graph as a look up table, notes the contribution per term, and sums them together with the learned intercept to make a prediction. In regression, the intercept is the mean target (label) of the training set, and each term adds or subtracts to this mean. In classification, the intercept reflects the base rate of the positive class on a log scale. The gray above and below the graph shows the confidence of the model in that region of the graph.

Local Explanations

We can see the full breakdown of a prediction on a single sample with Local Explanations. Here’s how to compute the prediction breakdown for the first sample in our dataset:

from interpret import show
show(ebm.explain_local(X[:1], y[:1]), 0)

Let’s take a look at the prediction by selecting it in the drop-down menu.

The model prediction is 188.50. We can see that the intercept adds about +151.9, bp subtracts about 0.02, and age adds about 0.04. If we repeat this process for all the terms, we’ll arrive exactly at the model prediction of 188.50.

Viewing _all_ term importances

Due to space limitations in our graphs, the term importance summary only shows the top 15 terms. To view the overall importances of all terms of a trained EBM - the scores shown in the global explanation summary - we use term_importances():

importances = ebm.term_importances()
names = ebm.term_names_

for (term_name, importance) in zip(names, importances):
    print(f"Term {term_name} importance: {importance}")

Term age importance: 5.001311528948614
Term sex importance: 6.708523327517389
Term bmi importance: 17.642397675657218
Term bp importance: 9.396838172373227
Term s1 importance: 2.0020402810254785
Term s2 importance: 3.540600886428829
Term s3 importance: 7.9769187029030935
Term s4 importance: 6.5972788273211735
Term s5 importance: 16.9036504189978
Term s6 importance: 6.712156145223616
Term age & s3 importance: 0.6758381224837813
Term age & s5 importance: 0.8299562591334948
Term bmi & bp importance: 0.7160110927851984
Term bmi & s2 importance: 0.6193972933066461
Term bmi & s4 importance: 0.9979264256393093
Term bmi & s5 importance: 0.5667737849391206
Term bp & s1 importance: 0.5356489634368404
Term s1 & s5 importance: 0.7019012395807438
Term s2 & s5 importance: 0.6657966220813195
Term s5 & s6 importance: 0.8689267033757884

Note that mean absolute contribution isn’t the only way of calculating term importances. Another metric our package provides is the min_max option, which computes the difference between the max (the highest score on the graph) and min (the lowest score on the graph) values for each term. Term importance measured with min_max is a measure of the maximum impact a term can have, even though it might have this amount of impact on very few cases, whereas avg_weight(the default parameter) is a measure of typical (average) contribution of a term across all cases.

importances = ebm.term_importances("min_max")
names = ebm.term_names_

for (term, importance) in zip(names, importances):
    print(f"Term {term} importance: {importance}")

Term age importance: 23.35947518196582
Term sex importance: 13.4711064997133
Term bmi importance: 86.65413537647615
Term bp importance: 68.38075820909529
Term s1 importance: 16.423270925189627
Term s2 importance: 23.783906073926055
Term s3 importance: 45.705132814559946
Term s4 importance: 40.002401019885575
Term s5 importance: 51.71758329930087
Term s6 importance: 41.50172750753319
Term age & s3 importance: 6.234581306088605
Term age & s5 importance: 5.017709065915959
Term bmi & bp importance: 6.098682054997774
Term bmi & s2 importance: 6.3367513027685245
Term bmi & s4 importance: 4.749804644651568
Term bmi & s5 importance: 4.0690996233663626
Term bp & s1 importance: 4.813833542635586
Term s1 & s5 importance: 8.831442355946336
Term s2 & s5 importance: 3.7834234767518775
Term s5 & s6 importance: 9.23554297122693

Feature/Term Group Importances

We provide utility functions to compute the importances of groups of features or terms and, optionally, append these importances to the global feature attribution bar graph. Note that shape function graphs are not generated for groups of features/terms, just their overall importance is shown on the Summary.

Grouping terms and then calculating and displaying their importance does not change the model and the predictions it makes in any way – group importances are just a method for computing the importance of groups of terms in addition to the importances of individual terms that are already calculated. As you’ll see in the examples below, it’s OK for features/terms to overlap in different groups.

Computing group importances

Let’s use the Adult dataset and train an EBM for a classification task.

import numpy as np
import pandas as pd
from interpret.glassbox import ExplainableBoostingClassifier

df = pd.read_csv(
    "https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data",
    header=None)
df.columns = [
    "Age", "WorkClass", "fnlwgt", "Education", "EducationNum",
    "MaritalStatus", "Occupation", "Relationship", "Race", "Gender",
    "CapitalGain", "CapitalLoss", "HoursPerWeek", "NativeCountry", "Income"
]
X = df.iloc[:, :-1]
y = df.iloc[:, -1]

adult_ebm = ExplainableBoostingClassifier()
adult_ebm.fit(X, y)

ExplainableBoostingClassifier()

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We then create a list of terms – single features or interactions – as our group and compute its importance:

from interpret.glassbox._ebm._research import *

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
importance = compute_group_importance(social_feature_group, adult_ebm, X)
print(f"Group: {social_feature_group} - Importance: {importance}")

Group: ['MaritalStatus', 'Relationship', 'Race', 'Gender', 'NativeCountry'] - Importance: 1.3018233812586584

In this example we create a group with five terms and compute its importance. Similar to single feature importances, we interpret this score as the average absolute contribution this group of terms makes when predicting across the training dataset. Note that for each prediction, the contribution of each term in the group will be added before taking the absolute value.

We also have the option to create a global explanation containing the group importance or append it to an existing explanation:

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
show(my_global_exp)

The importance of social_feature_group is about 1.30, which is higher than the importance of any individual feature/term:

We could make this type of comparison between different groups too:

education_feature_group = ["Education", "EducationNum"]
relationship_feature_group = ["MaritalStatus", "Relationship"]
social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(education_feature_group, adult_ebm, X, global_exp=my_global_exp)
my_global_exp = append_group_importance(relationship_feature_group, adult_ebm, X, global_exp=my_global_exp)
show(my_global_exp)

The importance of education_feature_group is about 0.52, higher than each of its individual terms but smaller than some individual terms such as Age. Remember, creating groups of features/terms does not, in any way, change the model and its predictions, it only allows you to estimate the importance of these groups.

This graph, for example, suggests that features related to relationships are more important than features reated to education.

We can also compare a group we are interested in (e.g. social_feature_group) with a group of all other reamining terms.

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
all_other_terms = [term for term in adult_ebm.term_names_ if term not in social_feature_group]

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(all_other_terms, adult_ebm, X, group_name="all_other_terms", global_exp=my_global_exp)
show(my_global_exp)

Note that all_other_terms has the highest importance score, followed by social_feature_group.

It’s even possible to create a group with all terms.

all_terms_group = [term for term in adult_ebm.term_names_]
mew_global_exp = append_group_importance(all_terms_group, adult_ebm, X, group_name="all_terms")
show(mew_global_exp)

Finally, we also expose a function to compute the importances of a group of terms as well as all the model’s original terms.

my_dict = get_group_and_individual_importances([social_feature_group, education_feature_group], adult_ebm, X)
for key in my_dict:
    print(f"Term: {key} - Importance: {my_dict[key]}")

Term: MaritalStatus, Relationship, Race, Gender, NativeCountry - Importance: 1.3018233812586584
Term: Age - Importance: 0.7281104362544496
Term: MaritalStatus - Importance: 0.6224365058032497
Term: CapitalGain - Importance: 0.5527273887812679
Term: Education, EducationNum - Importance: 0.5231765173944035
Term: Relationship - Importance: 0.5049287744637614
Term: Occupation - Importance: 0.37812843917977534
Term: Gender - Importance: 0.3729559159348626
Term: EducationNum - Importance: 0.3414948534209806
Term: HoursPerWeek - Importance: 0.29044595269343004
Term: Education - Importance: 0.21764230578473676
Term: CapitalLoss - Importance: 0.14941857970560227
Term: WorkClass - Importance: 0.12710829541530724
Term: fnlwgt - Importance: 0.1192080273594916
Term: NativeCountry - Importance: 0.07498287833289664
Term: Race - Importance: 0.06455281676770322
Term: MaritalStatus & HoursPerWeek - Importance: 0.06034030758853726
Term: Relationship & HoursPerWeek - Importance: 0.04664226944691118
Term: EducationNum & MaritalStatus - Importance: 0.03281998426632417
Term: Age & HoursPerWeek - Importance: 0.03141723695393752
Term: Age & CapitalLoss - Importance: 0.026932711264772768
Term: Age & Relationship - Importance: 0.026036035404428996
Term: Age & fnlwgt - Importance: 0.026008808858453462
Term: EducationNum & Occupation - Importance: 0.01723580992040829
Term: Relationship & CapitalLoss - Importance: 0.01060068857755741
Term: WorkClass & Race - Importance: 0.009299902576875274